The required, there were 25 chickens and 12 pigs on Old MacDonald's farm.
To solve this problem, we can use a system of equations to represent the number of chickens and pigs on Old MacDonald's farm. Let x be the number of chickens and y be the number of pigs. Then we have:
x + y = 37 (equation 1)
2x + 4y = 98 (equation 2)
Equation 1 represents the total number of animals, and Equation 2 represents the total number of legs. We can simplify equation 2 by dividing both sides by 2:
x + 2y = 49 (equation 3)
Now we have two equations with two variables. We can solve for x and y by using substitution or elimination. Let's use elimination by multiplying equation 1 by 2 and subtracting it from equation 3:
x + 2y = 49
-2x - 2y = -74
x = -25
Solving for x, we get:
x = 25
Substituting x = 25 into equation 1, we get:
25 + y = 37
Solving for y, we get:
y = 12
Therefore, there were 25 chickens and 12 pigs on Old MacDonald's farm.
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The equations are c + p = 37 and 2c + 4p = 98. Solving the system of equations the numbers are 26 and 11, respectively.
Explanation:To solve this problem, we can use a system of equations.
Let's assume that the number of chickens is represented by 'c' and the number of pigs is represented by 'p'. Based on the given information, we can create two equations:
1. c + p = 37 (equation 1)
2. 2c + 4p = 98 (equation 2)
We have two equations with two variables, so we can solve this system of equations to find the values of 'c' and 'p'.
Using equation 1, we can express 'c' in terms of 'p': c = 37 - p.
Substituting this into equation 2, we get: 2(37 - p) + 4p = 98. Solving this equation, we find: p = 11.
Substituting the value of 'p' back into equation 1, we find: c = 26.
Therefore, Old MacDonald had 26 chickens and 11 pigs on his farm.
Michelle has read 0.05625 percent of a book. If she has read 18 pages, how many total pages are in the book?
Explain how to translate the statement into an equation. Use n for the variable. Sixty-three is the product of nine and a number.
Answer:
Sample Response: Replace the word "is" with an equals sign. Replace the word "product" with a multiplication sign. Replace the words "a number" with the variable n, to represent the unknown value. The equation is 63 = 9n.
The statement 'Sixty-three is the product of nine and a number' translates to the equation 63 = 9 × n. The variable n represents the unknown number that, when multiplied by nine, equals sixty-three.
To translate the statement "Sixty-three is the product of nine and a number" into an equation using n for the variable, we can use the following steps:
1. Identify the unknown number: Let's denote the unknown number as n
2. Express the known quantities: We know that "Sixty-three" is equal to the product of "nine" and the unknown number n .
3. Write the equation: The statement can be translated into the equation:
[tex]\[ 63 = 9 \times n \][/tex]
In this equation:
- 63 represents the product of 9 and n .
- 9 represents the known quantity.
- n represents the unknown number we are trying to find.
So, the equation [tex]\( 63 = 9 \times n \)[/tex]expresses the statement "Sixty-three is the product of nine and a number" using the variable n .
What are the solutions to the equation x² = 625?
Select EACH correct answer.
A. -312.5
B.-25
C.25
D. 312.5
The three angle bisectors of ΔABC meet at P. Drag the vertices around to form different triangles, and then make a conjecture. Which segments appear to be equal in length? Check all that apply. XP = YP for an acute triangle XP = ZP for an acute triangle YP = ZP for an obtuse triangle ZP = XP for a right triangle XP = YP for an obtuse triangle
From a group of 5 candidates, a committee of 2 people is selected. In how many different ways can the committee be selected?
From a group of 5 candidates, a committee of 2 people is selected. In how many different ways can the committee be selected?
There are 10 different ways to select a committee of 2 people from a group of 5 candidates.
Explanation:To calculate the number of ways to select a committee of 2 people from a group of 5 candidates, we can use the combination formula. The number of combinations of n items taken r at a time is given by the formula:
nCr = n! / (r!(n-r)!)
Here, n is the total number of candidates (5) and r is the number of people to be selected for the committee (2). Plugging in the values, we get:
5C2 = 5! / (2!(5-2)!)
Simplifying this expression:
5C2 = (5 * 4) / (2 * 1)
Therefore, there are 10 different ways to select the committee.
Factor the quadratic equations W^2-W-12
Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row, and Lorraine has gotten 13. How many more jumps (j) do they need to match the record? Show your work!
1. Billy had 40 songs on his MP3 player. If he deleted 8 songs, what is the ratio of songs he kept to songs he deleted?
1 point
8:40
32:40
40:32
40:8
2. A vendor sold 63 hotdogs during a football game. If the ratio of hotdogs to hamburgers sold was 9:5, how many hamburgers did the vendor sell? *
1 point
Your answer
3. Paul had sold 24 orange fish. If the ratio of blue fish to orange fish is 3:8, how many fish did he sell in total?
1 point
Your answer
4. Jack has a collection of toy cars. If there are 2 blues, 5 black, 7 red and 3 purple cars, what is the ratio of purple to all the cars?
1 point
3:14
3:17
5. At an ice cream shop the ratio of sugar cones to waffle cones sold is 2:1. If there are 15 cones altogether, how many sugar cones are there?
1 point
3
5
15
10
6. There is a total of 72 total students. If the ratio of boys to girls is 4 to 5, how many of the students are girls?
1 point
32
40
8
7. Paul can walk 15 steps in 5 minutes. How long does it take Paul to walk 75 steps?
1 point
25
225
3
8. If the ratio of pink flower to blue flower is 2 to 7 and there are 12 pink flowers, how many blue flowers are there?
1 point
6
12
42
36
Other:
9. If the ratio of white pens to green pens is 1 to 4 and there are 6 white pens, how many are green?
1 point
6
20
24
36
10. Jennifer and Melissa are both making lemonade. Melissa uses 3 cups water to 1 cup lemon juice. Jennifer uses 5 cups water to 2 cups lemon juice. Which mixture will have more lemon flavor?
1 point
Jennifer's
Melissa's
11. Nicholas has a collection of pens. He has 4 red, 9 blues, 2 white and 3 black pens. What is the ratio of black to the total amount of pens in simplified form?
1 point
1:3
1:6
3:1
6:1
Which of the numbers is rational? A) π B) 25 C) 2 D) 3
Answer:
25, 2, & 3 are rational numbers
π is a irrational number.
Explanation:
I think we need to find out the irrational number.
Here we learn main difference between rational and irrational number.
Rational Number:
All numbers whose written in fraction form where numerator and denominator are whole number.
All the whole numbers are rational number.
For example: 2 (because we can write 2 as [tex] \frac{2}{1} [/tex]), [tex] \frac{5}{6} [/tex] etc
0.666666.... (endless repeating digits)
In given question: 25, 2 and 3 are rational numbers
Irrational Numbers:
All numbers that are not rational are considered irrational. An irrational number can be written as a decimal form, but not as a fraction form.
An irrational number has endless non-repeating digits to the right of the decimal point.
π = 3.141592...... (endless non repeating digits)
√2 =1.414213... (endless non repeating digits)
Answer:
25, 2, 3
Step-by-step explanation:
A rational number is a terminating decimal or a non-terminating, repeating decimal.
25, 2, and 3 are terminating decimals, so they are rational.
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. y = 2.5 when x = 9 answer asap plaese
Answer:
k = 22.5; xy = 22.5
your welcome
XD
The name of a triangle whose angles are all more that 90 degrees?
Acute
Obtuse
Right
Isosceles
None of the above
Answer:
Option B is correct.
Obtuse triangle.
Step-by-step explanation:
Acute triangle:
In acute triangle, all angles are less than 90 degree.
Obtuse triangle:
In obtuse triangle, the triangle has an angle more than 90 degree.
Right triangle.
In right triangle, it has a right angle 90 degree.
Isosceles triangle.
In isosceles triangle, it can be acute, right or obtuse depends only on the apex angle.
Therefore, the triangle whose angles are all more that 90 degree is, Obtuse triangle.
What is 4 equal parts
You purchase an item to sell in your store. The item costs you $6.45. You mark the item up 20%, but later run the item on sale at 5% off the marked price.If your customer must pay 6% sales tax, what will be the total amount paid by the customer for the item?
how would I solve for x?
Bryan purchases a new boat. The expression below represents the value of the boat after x years. 22000(.88)^(x+2) Which statement is true?
A.The price of the boat decreases by 88% every year.
B.The price of the boat increases by 88% every year.
C.The price of the boat decreases by 12% every year.
D.The price of the boat increases by 12% every year.
The formula for the growth rate is given by
[tex] y=a(b)^x [/tex]
Now when b is greater than 1 , then it is increasing function
and when b is less than 1 , then it is decreasing function.
Now in the function
[tex] 22000(.88)^{(x+2)} [/tex]
here value of b is 0.88 , which is less than 1 , so it is decreasing function
And decay rate is given by
1-r = 0.88
Subtract 1 from both sides
-r = 0.88-1
-r = -0.12
r = 0.12
or r= 12%
It means it is decreasing at a rate of 12%
Hence Option C is correct
C.The price of the boat decreases by 12% every year.
Jacqueline's piggy bank contains $6.20 in dimes and quarters. There are 32 coins in all. How many of each kind are there?
The length of a football field is 100 yards and the width is 53 yards. in the first game of the season, joe don catches the opening kickoff at the corner of the goal line and runs straight as a string the diagonal length of the field to score a touchdown. the next day, the local paper credits joe for a 100 yard touchdown run, but how far did he actually run?
Answer:
Joe Don actually ran 113.2 yards
Step-by-step explanation:
Length of the football field = 100 yd
Width of the football field = 53 yd
The football field is rectangular in shape. So in order to find the diagonal of the field, we need to split it up into two right triangles.
In one of the right triangles, the length and width becomes the two sides of it and diagonal is the third side.
In order to find the third side (diagonal), we need to apply the Pythagoras theorem.
So,
Diagonal² = 100² + 53²
Diagonal² = 10000 + 2809
Diagonal² = 12809
Taking square root on both sides
[tex]\sqrt{Diagonal^{2} } =\sqrt{12809}[/tex]
Diagonal = 113.17 yd
Diagonal = 113.2 yd (approx)
Thus Joe Don actually ran 113.2 yards
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find the inverse of y=x2-10x
y = x^2 - 10x + 25 - 25
y = (x-5)^2 - 25
y+25 = (x-5)^2
x-5 = +/-sqrt(y+25)
And you get TWO inverses:
x = 5 + sqrt(y+25), for x>=5
x = 5 - sqrt(y+25), for x<=5
Answer:
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Step-by-step explanation:
We are asked to find the inverse for the function [tex]y=x^2-10x[/tex].
We know that to find inverse, we interchange x and y values and then solve for y.
After interchanging x and y values, we will get:
[tex]x=y^2-10y[/tex]
Switch sides:
[tex]y^2-10y=x[/tex]
[tex]y^2-10y-x=x-x[/tex]
[tex]y^2-10y-x=0[/tex]
Now, we will use quadratic formula to solve for y.
[tex]y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}[/tex]
[tex]y=\frac{10\pm \sqrt{100+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4*25+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4(25+x)}}{2}[/tex]
[tex]y=\frac{10\pm 2\sqrt{(25+x)}}{2}[/tex]
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Therefore, the inverse function for our given function would be [tex]y=5\pm \sqrt{(25+x)}[/tex].
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 5 7.5 15 7.5 11 13.8 6.4
HS 16 0 9.5 14.5 5 13 . 10.7 5.3
Which of the choices below best describes how to measure the spread of this data? (Hint: Use the minimum and maximum values to check for outliers.) (2 points) A:Both spreads are best described with the IQR.
B:Both spreads are best described with the standard deviation.
C:The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D:The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answer:
Option A is correct
Step-by-step explanation:
Given is a table which shows data from a survey about the amount of time students spend doing homework each week.
College HS
High 50 16
Low 5 0
Q1 7.5 9.5
Q3 15 14.5
IQR 7.5 5
Median 11 13
Mean 13.8 10.7
Std dev 6.4 5.3
1.5IQR 11.25 7.5
Q1-1.5IQR -9.38 -12
Q3+1.5IQR 37.5 29.5
WE find that there is only one outlier in college with 50 as high.
Except that all others are well within IQR range. Hence outliers are minimum
So option A is right.
Final answer:
To determine the spread of data on student homework hours, IQR and standard deviation are used. The college data's spread is best described by IQR, while the high school data's spread is best described by standard deviation, making Option C the most suitable choice.
Explanation:
To measure the spread of the data for the amount of time students spend doing homework each week, we have two primary measures: the Interquartile Range (IQR) and the standard deviation (σ). IQR represents the difference between the third quartile (Q3) and the first quartile (Q1) and describes the spread of the middle 50% of the data. The standard deviation indicates how much the values in the dataset deviate from the mean, which can help in understanding the overall spread including potential outliers.
When dealing with outliers, it's important to consider that potential outliers are typically identified as values that are more than 1.5 × IQR above Q3 or below Q1. We would use the minimum (Low) and maximum (High) values provided alongside the IQR to check for outliers. For the college data, with a High of 50 and a Low of 5, the range is 45. For high school, the range is 16. Outliers could potentially affect the standard deviation significantly, making IQR a better measure for the middle spread of data.
Based on this, the college data with a wider range may be more affected by outliers, whereas the high school data with a smaller range may not. Therefore, the spread for the college data can be better described by the IQR, while the standard deviation can be a good measure for the high school data. This suggests that Option C: "The college spread is best described by the IQR. The high school spread is best described by the standard deviation." is the most suitable choice.
A 45° sector in a circle has an area of 13.75π cm². What is the area of the circle? Use 3.14 for pi.
Enter your answer as a decimal in the box.
cm²
Area of circle is 345.4 cm²
Area of sector:Given that;
Angle of sector = 45°
Area of sector = 13.75π cm²
Find:
Area of the circle
Computation:
Area of sector = [tex]\frac{\theta}{360}[/tex][Area of circle]
13.75π = [tex]\frac{\theta}{360}[/tex][Area of circle]
13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]
13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]
43.175 = 0.125[Area of circle]
Area of circle = 345.4 cm²
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Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition?
A. 2 + x + 3y
B. (2 + x) + 3y
C. 2x + (3 + y)
D. x + (2 + 3y)
Eric borrowed $1,800 for 9 months at 13.5% simple interest under an
add-on plan. What was his monthly payment?
a. $15.63
b. $220.25
c. $187.50
d. $1,982.25
ANSWER IS NOT C
Consider the polynomial: x/4– 2x^5 + x^3/2 + 1 Which polynomial represents the standard form of the original polynomial?
a.x^3/2 – 2x^5 + x/4 + 1
b.–2x^5 + x^3/2 + x/4 + 1
c. –2x^5 + x/4 + x^3/2 + 1
d. 1 – 2x^5 + x^3/2 + x/4
Answer:
b. –2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
In the given expression, the degrees of the terms, in the order given, are ...
1, 5, 3, 0
When the terms are properly arranged in standard form, they will be ...
5, 3, 1, 0 . . . . descending order
The standard form of this expression is ...
-2x^5 +x^3/2 +x/4 +1 . . . . . . matches choice B
Answer: b.–2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.
{-4, 12, -36, ...}
Write an expression for the following situation and solve it. Mr. Simms bought 20 pencils. He used 1/4 of the pencils and then gave 4 to his students.
Isabella is solving the equation 4x^2=13x−3 with the quadratic formula.
Which values could she use for a, b, and c?
A. a = 4, b = −13, c = 3
B. a = 4, b = 3, c = −13
C. a = 4, b = 13, c = −3
D. a = 4, b = −3, c = 13
values could she use for a, b, and c a = 4 b = -13 c = 3
Step-by-step explanation:
We have been given the equation
4x²=13x-3
Subtract 4x² to both sides of the equation
0=-4x²+13x-3
Multiply both sides of the equation by -1
4x²-13x+3=0
The general equation of a quadratic equation is ax²+ bx +c=0
Comparing this equation with above equation 4x²-13x+3=0
a = 4
b = -13
c = 3
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The function f(x)=-√-x is shown on the graph. Which statement is correct? The range of the graph is all real numbers greater than or equal to 0. The domain of the graph is all real numbers greater than or equal to 0. The range and domain of the graph are the same. The domain of the graph is all real numbers.
The correct option is: The range and domain of the graph are the same.
Explanation
Given function is: [tex]f(x) = -\sqrt{-x}[/tex]
The inside term of a square root can't be negative, it will be always 0 or positive. That means, [tex]-x \geq 0[/tex] or [tex]x\leq 0[/tex]
So, the Domain of the function is : "All real numbers such that [tex]x\leq 0[/tex]"
Now, if x=0, then f(x) =0 and if x is any negative number, then f(x) will be also negative.
That means, the Range of the function: "All real numbers such that [tex]f(x)\leq 0[/tex]"
So, the range and domain of the function are the same.
Solve for a.
(a+6)^2=49
A −13 and 1
B −3 √6 and 3 √6
C −1 and 13
D −√43 and √43
The solutions for a are a=1 and a=−13. So the correct answer is A. -13 and 1.
To solve the equation [tex]\( (a+6)^2 = 49 \)[/tex], follow these steps:
1. Take the square root of both sides:
[tex]\[ \sqrt{(a+6)^2} = \sqrt{49} \][/tex]
2. Consider both positive and negative roots:
[tex]\[ a + 6 = \pm 7 \][/tex]
3. Solve for ( a ):
For ( a + 6 = 7 ):
[tex]\[ a = 7 - 6 = 1 \][/tex]
For ( a + 6 = -7 ):
[tex]\[ a = -7 - 6 = -13 \][/tex]
So, the solutions for ( a ) are ( a = 1 ) and (a = -13).
Therefore, the correct answer is A. -13 and 1.
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